One of the most difficult places to keep shiny is the end of a chrome exhaust tip. Heated hydrocarbons and other nasty things can quickly bake on and blacken a once shiny chrome or stainless tip.
To quickly (I'm very much into speed!) get the surface to a high shine I use Never-Dull. Never-Dull is a solution-embedded cloth fibre wadding that comes in a small tin. You simply pull off some wadding (Kind of like heavy duty cotton candy) and polish the surface. The wadding is exceptionally useful for stubborn chrome problems like tail pipes, headers lug nuts, stainless pipes, spokes, brake lines, hose clamps, etc. Any non-clearcoated metal surface.